1. Field of the Invention
This invention relates to satellite positioning systems (SPS), and in particular, to determining time associated with SPS signal transmission and/or reception.
2. Background Information
SPS receivers such as GPS (Global Positioning System) receivers normally determine their position by computing relative times of arrival of signals transmitted simultaneously from a multiplicity of satellites such as GPS (or NAVSTAR) satellites. In typical satellite positioning systems, such as GPS, the multiplicity of satellites are synchronized according to a highly accurate system clock, which may provide atomic clock accuracy. Generally, each satellite transmits navigational data (e.g., the location of the satellite) that also includes a time stamp to indicate when the data was transmitted, according to the time as indicated by the system clock (referred to hereafter as system time), which, in the case of GPS, is referred to as (GPS) system time.
However, SPS receivers typically do not have such an accurate clock. Thus, an SPS receiver typically determines timing information by reading and timing information contained in the satellite message. Many receivers determine position and time by using measurements from four (or more) satellites. The range to each of four satellites (i=1, 2, 3, 4) may be expressed as: ##EQU1##
wherein
x, y, and z are the coordinates/position of the receiver (unknown); PA1 xi, yi, and zi are the ith satellite's coordinates/position (known); and PA1 cb represents the clock bias, which is a result of the error in time between the clock of the receiver and the reference time (unknown). PA1 .DELTA.PRi is the pseudorange residual for the ith satellite (i=1, 2, 3, 4), and represents a difference between the measured pseudorange and an initial estimated range to the ith satellite (known); PA1 uxi, uyi, and uzi are the direction cosines of the line-of-sight (LOS) vector from the receiver to the ith satellite, as projected along the x, y and z coordinate axes (known); PA1 .DELTA.x, .DELTA.y, .DELTA.z, and .DELTA.cb are the corrections to the initial estimates of coordinates/position and the clock of the receiver, which may be offset from a reference clock (unknown). PA1 H.sup.-1 is the inverse of the observation matrix; PA1 (H.sup.T.multidot.H).sup.-1 is the pseudoinverse of the observation matrix; and PA1 x is the least-squares estimate of the vector of unknown parameters, x.
Thus, there is typically a total of four unknowns in equation (1) above.
Often, PRi is referred to as a pseudorange, since it represents the actual range to the ith satellite, plus or minus an offset that may result due to the receiver's clock error, as indicated by the cb term in equation (1). The above equation, using measurements from four satellites, may be linearized and expressed in matrix form as follows: ##EQU2##
wherein
Hereinafter, the pseudorange residual vector is also referred to as Z, the n.times.4 element matrix H is also referred to as an observation matrix, and x represents the SPS receiver position and time correction vector, which contains the unknowns of interest. Thus, if an inverse of the observation matrix H exists, a unique solution to unknown x in the set of linear equations represented by the above matrix equation (2) may be determined, such that: EQU x=H.sup.-1.multidot.Z
or EQU x=(H.sup.T.multidot.H).sup.-1 H.sup.T.multidot.Z (3)
wherein,
To determine the pseudoranges (PRi), a conventional SPS receiver typically uses an initial estimate of its position and clock bias that is known to within a millisecond. However, since signals from satellites travel at or approximately the speed of light, even a 1 millisecond ambiguity in time may result in an error of up to 300 kilometers in the pseudorange measurement. By solving the matrix equation (2) above, the conventional GPS receiver may compute a correction to its initial clock bias estimate, wherein the initial clock bias estimate is derived by reading the navigational message which provides "time-alignment" information.
Unfortunately, in many situations, determining the system time by reading the navigation message of one or more satellites may be difficult, due signal quality degradation. For example, where there is blockage of the satellite signals, the received signal level or signal-to-noise ratio (SNR) from the GPS satellites may be too low to demodulate and read the satellite data signals without error. Such situations may arise in personal tracking and other highly mobile applications. Under such signal conditions, it is possible for a receiver to still acquire and track the GPS signals. However, performing location and unambiguous time measurement without timing data may be best performed using alternative methods.
The present invention provides a method and apparatus for determining time in an SPS, such as the time of satellite transmission and/or time of measurement by an SPS receiver, relative to a reference time (e.g., system time or other relatively accurate reference time) without the need to determine the reference time from processing timing information provided within the satellite navigational data message.